1. Field of the Invention
The present invention relates to a control apparatus, a lithography apparatus, and a method of manufacturing an article.
2. Description of the Related Art
FIG. 24 is a block diagram of a typical 2-degrees-of-freedom control system. Referring to FIG. 24, a transfer function from an input (target value) r to an output (controlled variable) y is given by:
                    y        =                              (                                          KP                                  1                  +                  KP                                            +                              FP                                  1                  +                  KP                                                      )                    ⁢          r                                    (        1        )            where the first term on the right side is a feedback (FB) term, and the second term on the right side is a feed-forward (FF) term. The difference between the target value r and the controlled variable y is a control error e, and the 2-degrees-of-freedom control system is intended to set the control error e to zero (bring the control error e close to zero).
Referring to equation (1), as is apparent from y=r for F=1/P, when the transfer function (FF gain) of an FF controller is defined as the inverse function of the transfer function (characteristic) of a controlled object, it is possible to attain an ideal target value response (a reduction in control error). In this manner, highly accurate modeling of the controlled object (highly accurate representation of the controlled object using a transfer function and numerical values) determines the performance of the target value response.
In modeling the controlled object, the controlled object is commonly known to be expressed as a polynomial of a Laplace operator s. As long as the controlled object can be accurately expressed as a polynomial of the Laplace operator s, its inverse function can also be expressed as a polynomial of the Laplace operator s, thus allowing optimum FF control. In the field of moving body control, it has been reported that the target value response is improved by FF of the first-order derivative (velocity) and second-order derivative (acceleration) of the target position (further, FF of the third-order derivative (jerk) and fourth-order derivative of the target position). However, it is difficult to express the characteristic of the controlled object as a polynomial of the Laplace operator s with perfect accuracy. Also, although not only a modeling technique which uses a polynomial of the Laplace operator s, but also various modeling techniques have been attempted earlier, the controlled object cannot be modeled with perfect accuracy in any of these modeling techniques, so it is impossible to prevent modeling errors.
A change in characteristic of the controlled object is one factor of the modeling errors. For example, in moving body control for moving a carrier, the characteristic of the controlled object changes depending on both the weight of a load and the state of a road surface. Japanese Patent Laid-Open No. 2009-237916 proposes a technique of preparing several models to select an appropriate model based on an actual response, instead of exclusively using one model for the controlled object, to cope with such a change in characteristic of the controlled object.
In a control system typified by a 2-degrees-of-freedom control system, the performance of a target value response depends on the accuracy of modeling the controlled object, as described above. Hence, as the performance required for the control system becomes higher, the controlled object needs to be modeled with a higher accuracy, so a considerable load is imposed on the modeling operation. A reduction in modeling error by the technique described in Japanese Patent Laid-Open No. 2009-237916 is constrained by models prepared in advance.